Results 1 to 10 of about 222 (166)

Ostrowski and Čebyšev type inequalities for interval-valued functions and applications. [PDF]

PLoS ONE, 2023
As an essential part of classical analysis, Ostrowski and Čebyšev type inequalities have recently attracted considerable attention. Due to its universality, the non-additive integral inequality takes several forms, including Sugeno integrals, Choquet ...
Jing Guo, Xianjun Zhu, Wenfeng Li, Hui Li   +3 more
doaj   +2 more sources

Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator [PDF]

Heliyon
Convexity and fractional integral operators are closely related due to their fascinating properties in the mathematical sciences. In this article, we first establish an identity for the modified Atangana-Baleanu (MAB) fractional integral operators. Using
Gauhar Rahman, Muhammad Samraiz, Kamal Shah, Thabet Abdeljawad, Yasser Elmasry   +4 more
doaj   +2 more sources

New generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity [PDF]

Journal of Inequalities and Applications, 2017
The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green’s functions.
Nasir Mehmood, Ravi P Agarwal, Saad Ihsan Butt, Josip Pečarić   +3 more
doaj   +2 more sources

On the Generalization of Ostrowski-Type Integral Inequalities via Fractional Integral Operators with Application to Error Bounds

Fractal and Fractional, 2023
The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The Ostrowski’s type inequality is frequently used to investigate errors in numerical quadrature rules and computations.
Gauhar Rahman, Miguel Vivas-Cortez, Çetin Yildiz, Muhammad Samraiz, Shahid Mubeen, Mansour F. Yassen   +5 more
doaj   +1 more source

Ostrowski Type Inequalities for s-Convex Functions via q-Integrals

Journal of Function Spaces, 2022
The new outcomes of the present paper are q-analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s-convex mappings.
Khuram Ali Khan, Allah Ditta, Ammara Nosheen, Khalid Mahmood Awan, Rostin Matendo Mabela   +4 more
doaj   +1 more source

Inequalities of Ostrowski–Grüss type and applications [PDF]

Applicationes Mathematicae, 2002
Some new inequalities of Ostrowski-Gruss type are derived. They are applied to the error analysis for some Gaussian and Gaussian-like quadrature formulas.
Tuna, Adnan, Daghan, Durmus
  +7 more sources

Ostrowski type inequalities involving conformable integrals via preinvex functions

AIP Advances, 2020
In this research article, we use preinvex functions to develop Ostrowski type inequalities for conformable integrals. First, we aim for an identity linked with the Ostrowski inequality.
Yousaf Khurshid, Muhammad Adil Khan, Yu-Ming Chu   +2 more
doaj   +1 more source

On a variant of Čebyšev’s inequality of the Mercer type

Journal of Inequalities and Applications, 2020
We consider the discrete Jensen–Mercer inequality and Čebyšev’s inequality of the Mercer type. We establish bounds for Čebyšev’s functional of the Mercer type and bounds for the Jensen–Mercer functional in terms of the discrete Ostrowski inequality ...
Anita Matković, Josip Pečarić
doaj   +1 more source

Generalizations of Hardy-Type Inequalities by Montgomery Identity and New Green Functions

Axioms, 2023
In this paper we extend general Hardy’s inequality by appropriately combining Montgomery’s identity and Green functions. Related Grüss and Ostrowski-type inequalities are also derived.
Kristina Krulić Himmelreich, Josip Pečarić, Dora Pokaz, Marjan Praljak   +3 more
doaj   +1 more source

Ostrowski Type Inequalities [PDF]

Proceedings of the American Mathematical Society, 1995
The following generalization of Ostrowski's inequality is given: Let \(f\in C^{n+1}([a,b])\), \(n\in\mathbb{N}\) and \(y\in [a,b]\) be fixed, such that \(f^{(k)}(y)=0\), \(k=1,\dots,n\). Then \[ \Biggl|{1\over b-a} \int^b_a f(t)dt- f(y)\Biggr|\leq {|f^{(n+1)}|_\infty\over (n+2)!} \Biggl({(y-a)^{n+2}+ (b-y)^{n+2}\over b-a}\Biggr).
openaire   +1 more source